📐 geometry

1. **Stating the problem:** We have a trapezoid ABCD with sides AD = 4.0 cm, DC = 2.0 cm, and AB = 5.0 cm. We need to find: a. The length of BC

1. **State the problem:** Calculate the area of one fence slat composed of a rectangle and a semi-circle on top. 2. **Given:**

1. **State the problem:** We have an isosceles triangle ABC with vertices B(0,0) and C(20,0) on the x-axis. The triangle's area is 240, and AB = AC. We need to find the y-coordinat

1. **Problem Statement:** A circle is drawn inside a regular hexagon such that no part of the circle lies outside the hexagon. The circle does not touch all six sides. We need to f

1. **Stating the problem:** We have a triangle with a vertical side of length 6 cm and a horizontal base of length 12 cm, which is divided into two smaller segments of 7.5 cm and 2

1. **State the problem:** Calculate the circumference $C$ of a circle with radius $r = 11.5$ inches. 2. **Formula:** The circumference of a circle is given by the formula:

1. **State the problem:** We are given a circle with a diameter of 8 ft and need to find its circumference. 2. **Formula:** The circumference $C$ of a circle is given by the formul

1. **State the problem:** We have triangle $\triangle CDE$ with vertices $C(-8,-8)$, $D(-2,-8)$, and $E(-5,-3)$, and its translation $\triangle C'D'E'$ with vertices $C'(-2,-2)$, $

1. **State the problem:** We have a triangle ABC with angles A, B, and C. Angle A is 21 degrees more than angle B, and angle C is 36 degrees more than angle B. We need to find angl

1. **State the problem:** Fill in the blanks for the angle relationships in the triangle.

1. **State the problem:** We need to find the length of the hypotenuse $c$ of a right triangle with legs measuring 6 meters and 8 meters. 2. **Formula used:** According to the Pyth

1. **State the problem:** We have a right triangle with legs of lengths 12 feet and 5 feet, and we need to find the length of the hypotenuse $c$. 2. **Formula used:** According to

1. **Problem statement:** Find the angle \(\angle XWZ\) in trapezium XYZW where \(XY=7\), \(WY=11\), \(WX=8\), and \(YZ=\) unknown but not needed. 2. **Understanding the trapezium:

1. **State the problem:** We have a right triangle with one angle of 30° and the leg opposite this angle labeled as $x - 3$. We need to solve for $x$. 2. **Recall the formula:** In

1. **State the problem:** Find the distance from the point $(2,5)$ to the circle given by the equation $$x^2 + y^2 - 6x - 4y - 3 = 0.$$\n\n2. **Rewrite the circle equation in stand

1. **Problem:** Find the surface area of a rectangular prism with length 11 cm, width 6 cm, and height 3 cm. 2. **Formula:** The surface area (SA) of a rectangular prism is given b

1. **State the problem:** Find the area of the irregular polygon composed of three simpler shapes: a vertical rectangle, a horizontal rectangle, and a trapezoid. 2. **Identify the

1. **State the problem:** We have an oblique triangular prism and a right cylinder with the same base area and volume. The prism's base is a triangle with an altitude of 8 and two

1. **Problem:** Calculate the area and perimeter of a triangle with sides 15.1 cm, 25.2 cm, and 10.9 cm, correct to one decimal place. 2. **Formula:**

1. **State the problem:** We are given the areas of the faces of a rectangular prism's net and need to find its dimensions (length, width, height) in inches. 2. **Given areas:** Th

1. The problem asks to find the perimeter of a shape, but the shape or its dimensions are not specified in the question. 2. The perimeter of a polygon is the sum of the lengths of